SOLUTION: A store has light bulbs from two suppliers, 1 and 2. The chance of supplier 1 delivering defective bulbs is 10% whereas supplier 2 has a defective rate of 3%. Suppose 60% of the cu

Question 344361: A store has light bulbs from two suppliers, 1 and 2. The chance of supplier 1 delivering defective bulbs is 10% whereas supplier 2 has a defective rate of 3%. Suppose 60% of the current supply of light bulbs came from supplier 1. If one of these bulbs is taken from the current supply and observed to be defective, find the probability that it came from supplier 2.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A store has light bulbs from two suppliers, 1 and 2. The chance of supplier 1 delivering defective bulbs is 10% whereas supplier 2 has a defective rate of 3%. Suppose 60% o0f the current supply of light bulbs came from supplier 1. If one of these bulbs is taken from the current supply and observed to be defective, find the probability that it came from supplier 2.
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P(2|d) = P(2 and d)/P(d)
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= [P(d|2)P(2)]/[P(d and 2) +P(d and 1)]
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= [P(d|2)P(2)]/[P(d|2)P(2)+P(d|1)*P(1)]
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= [0.03*0.4]/[0.03*0.4 + 0.1*0.6]
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= 0.012/[0.012+0.06]
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= 0.012/0.072
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= 0.1667
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Cheers,
Stan H.
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